CSPICE_DRDLAT computes the Jacobian of the transformation from latitudinal
to rectangular coordinates.
radius the distance of a point from the origin.
[1,n] = size(radius); double = class(radius)
lon the angle of the point measured from the XZ plane in radians.
The angle increases in the counterclockwise sense about the
[1,n] = size(lon); double = class(lon)
lat the angle of the point measured from the XY plane in radians.
The angle increases in the direction of the +Z axis.
[1,n] = size(lat); double = class(lat)
jacobi = cspice_drdlat( r, lon, lat)
jacobi the matrix of partial derivatives of the conversion between
latitudinal and rectangular coordinates, evaluated at the input
coordinates. This matrix has the form
If [1,1] = size(radius) then [3,3] = size(jacobi)
If [1,n] = size(radius) then [3,3,n] = size(jacobi)
double = class(jacobi)
| dx/dr dx/dlon dx/dlat |
| dy/dr dy/dlon dy/dlat |
| dz/dr dz/dlon dz/dlat |
evaluated at the input values of r, lon and lat.
Here x, y, and z are given by the familiar formulae
x = r * cos(lon) * cos(lat)
y = r * sin(lon) * cos(lat)
z = r * sin(lat).
It is often convenient to describe the motion of an object
in latitudinal coordinates. It is also convenient to manipulate
vectors associated with the object in rectangular coordinates.
The transformation of a latitudinal state into an equivalent
rectangular state makes use of the Jacobian of the
transformation between the two systems.
Given a state in latitudinal coordinates,
( r, lon, lat, dr, dlon, dlat )
the velocity in rectangular coordinates is given by the matrix
t | t
(dx, dy, dz) = jacobi| * (dr, dlon, dlat)
This routine computes the matrix
For important details concerning this module's function, please refer to
the CSPICE routine drdlat_c.
-Mice Version 1.0.0, 12-MAR-2012, EDW (JPL), SCK (JPL)
Jacobian of rectangular w.r.t. latitudinal coordinates